Least Common Multiple (LCM) of 36 and 199
The least common multiple (LCM) of 36 and 199 is 7164.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 36 and 199?
First, calculate the GCD of 36 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 199 = 0 remainder 36 |
| 2 | 199 ÷ 36 = 5 remainder 19 |
| 3 | 36 ÷ 19 = 1 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 11 | 1221 |
| 73 and 82 | 5986 |
| 104 and 104 | 104 |
| 76 and 75 | 5700 |
| 180 and 86 | 7740 |